I couldn't fix this either, but I did learn that running joy2key from a batch script (run as a "startup" program in HyperHQ), will allow me to use my controller when HyperSpin first boots without showing me annoying splash screens (xpadder run this way throws splash screens). Then keeping my RocketlauncherUI -> KeyMapper -> "Frontend profile" set to xpadder, and configuring xpadder for the HyperSpin main menu, lets me use controls after exiting games (no xpadder splash screens here either).
I run most of my emulators through RetroArch, so that it can handle controllers. The few systems RetroArch doesn't do so well, I set up xpadder configurations for and configure for Xbox controls. This is feasible since PS4 controllers are simulated on PC as Xbox (xinput) controllers via DS4Windows.
Pretty kludgy, but it seems ok so far